1) La descarga del recurso depende de la página de origen
2) Para poder descargar el recurso, es necesario ser usuario registrado en Universia


Opción 1: Descargar recurso

Opción 2: Descargar recurso

Detalles del recurso

Descripción

Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1+1D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1+1D, we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed v[subscript B]. We find that in 1+1D, the “front” of the OTOC broadens diffusively, with a width scaling in time as t[superscript 1/2]. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t[superscript 1/3] in 2+1D and as t[superscript 0.240] in 3+1D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2+1D. We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2+1D, our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1+1D, we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly. We also use this mapping to give exact results for entanglement growth in 1+1D circuits.

Pertenece a

DSpace at MIT  

Autor(es)

Haah, Jeongwan -  Nahum, Adam -  Vijay, Sagar - 

Id.: 71229256

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo de recurso: Article  -  http://purl.org/eprint/type/JournalArticle  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Creative Commons Attribution

Requerimientos técnicos:  Browser: Any - 

Relación: [IsBasedOn] American Physical Society
[References] http://dx.doi.org/10.1103/PhysRevX.8.021014
[References] Physical Review X

Fecha de contribución: 21-abr-2018

Contacto:

Localización:
* 2160-3308
* Nahum, Adam et al. "Operator Spreading in Random Unitary Circuits." Physical Review X 8, 2 (April 2018): 021014
* PUBLISHER_CC

Otros recursos del mismo autor(es)

  1. Deconfined Quantum Critical Points: Symmetries and Dualities The deconfined quantum critical point (QCP), separating the Néel and valence bond solid phases in a ...
  2. Emergence and spontaneous breaking of approximate $O(4)$ symmetry at a weakly first-order deconfined phase transition We investigate approximate emergent nonabelian symmetry in a class of weakly first order `deconfined...
  3. Quantum Entanglement Growth under Random Unitary Dynamics Characterizing how entanglement grows with time in a many-body system, for example, after a quantum ...
  4. Sample-optimal tomography of quantum states It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessar...
  5. Spurious long-range entanglement and replica correlation length Topological entanglement entropy has been regarded as a smoking-gun signature of topological order i...

Otros recursos de la mismacolección

  1. Ten years of genetics and genomics: what have we achieved and where are we heading? To celebrate the first 10 years of Nature Reviews Genetics, we asked eight leading researchers for t...
  2. Functional Association of Gdown1 with RNA Polymerase II Poised on Human Genes Most human genes are loaded with promoter-proximally paused RNA polymerase II (Pol II) molecules tha...
  3. Epigenomic analysis detects aberrant super-enhancer DNA methylation in human cancer Background: One of the hallmarks of cancer is the disruption of gene expression patterns. Many molec...
  4. Insulated Neighborhoods: Structural and Functional Units of Mammalian Gene Control Understanding how transcriptional enhancers control over 20,000 protein-coding genes to maintain cel...
  5. Stress from Nucleotide Depletion Activates the Transcriptional Regulator HEXIM1 to Suppress Melanoma Studying cancer metabolism gives insight into tumorigenic survival mechanisms and susceptibilities. ...

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.